If a-2-3-4k- and b-4-3-2k- find the angle between a and b-

We have, a·b=abcosθ ⇒cosθ=a·bab, where θ is angle between a and b. Now, a·b=a_xb_x+a_yb_y+a_zb_z ⇒a·b=2× 4+3× 3+4× 2=25 Also, | a |=√(a_x^2+a_y^2+a_z^2) ⇒ | a ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Section Formula

If a=2î+3ĵ+4k...

Question

If $\to a = 2^i + 3^j + 4^k$ and $\to b = 4^i + 3^j + 2^k$ , find the angle between $\to a$ and $\to b$ .

{cos}^{- 1} (\frac{25}{29})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

{cos}^{- 1} (\frac{23}{29})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

{cos}^{- 1} (\frac{20}{29})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

{cos}^{- 1} (\frac{18}{29})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A ${cos}^{- 1} (\frac{25}{29})$
We have, $\to a \cdot \to b = a b cos θ$
$\Rightarrow cos θ = \frac{\to a \cdot \to b}{a b},$ where $θ$ is angle between $\to a$ and $\to b$ .

Now, $\to a \cdot \to b = a_{x} b_{x} + a_{y} b_{y} + a_{z} b_{z}$
$\Rightarrow \to a \cdot \to b = 2 \times 4 + 3 \times 3 + 4 \times 2 = 25$

Also,
$∣ ∣ \to a ∣ ∣ = \sqrt{a_{x}^{2} + a_{y}^{2} + a_{z}^{2}}$
$\Rightarrow ∣ ∣ \to a ∣ ∣ = \sqrt{2^{2} + 3^{2} + 4^{2}} = \sqrt{29}$

and,

$∣ ∣ ∣ \to b ∣ ∣ ∣ = \sqrt{b_{x}^{2} + b_{y}^{2} + b_{z}^{2}}$
$\Rightarrow ∣ ∣ ∣ \to b ∣ ∣ ∣ = \sqrt{4^{2} + 3^{2} + 2^{2}} = \sqrt{29}$

Thus,
$cos θ = \frac{25}{29}$

$∴ θ = {cos}^{- 1} \frac{25}{29}$

Suggest Corrections

Similar questions

Q. For any three vectors

\to a, \to b

and

\to c

, prove that vectors

\to a - \to b, \to b - \to c

and

\to c - \to a

are coplanar.

Q. If

\to a

and

\to b

are vectors such that

| \to a + \to b | = \sqrt{29}

and

\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b

, then a possible value of

(\to a + \to b) \cdot (- 7^i + 2^j + 3^k)

\to A

and

\to B

represent force acting on a body in Newton.

\to A

has a magnitude of

3 N

. Then comment on the magnitude of

\to B

Q. If

[\to a \times \to b \to b \times \to c \to c \times \to a] = λ [\to a \to b \to c]^{2}

, then

λ

is equal to

Q. Consider three vectors

\to A =^i +^j - 2^k, \to B =^i -^j +^k

and

\to C = 2^i - 3 j + 4^k . A

vector

\to X

of the form

α \to A + β \to B

(

α

and

β

are numbers) in perpendicular to

\to C

. The ratio of

α

and

β

Join BYJU'S Learning Program

If →a=2^i+3^j+4^k and →b=4^i+3^j+2^k, find the angle between →a and →b.

If $\to a = 2^i + 3^j + 4^k$ and $\to b = 4^i + 3^j + 2^k$ , find the angle between $\to a$ and $\to b$ .